U.S. patent number 5,754,292 [Application Number 07/966,644] was granted by the patent office on 1998-05-19 for method and apparatus for measuring the intensity and phase of an ultrashort light pulse.
This patent grant is currently assigned to The Regents of the University of California, Sandia National Laboratory. Invention is credited to Daniel J. Kane, Rick P. Trebino.
United States Patent |
5,754,292 |
Kane , et al. |
May 19, 1998 |
**Please see images for:
( Certificate of Correction ) ** |
Method and apparatus for measuring the intensity and phase of an
ultrashort light pulse
Abstract
The pulse shape I(t) and phase evolution x(t) of ultrashort
light pulses are obtained using an instantaneously responding
nonlinear optical medium to form a signal pulse. A light pulse,
such a laser pulse, is split into a gate pulse and a probe pulse,
where the gate pulse is delayed relative to the probe pulse. The
gate pulse and the probe pulse are combined within an
instantaneously responding optical medium to form a signal pulse
functionally related to a temporal slice of the gate pulse
corresponding to the time delay of the probe pulse. The signal
pulse is then input to a wavelength-selective device to output
pulse field information comprising intensity vs. frequency for a
first value of the time delay. The time delay is varied over a
range of values effective to yield an intensity plot of signal
intensity vs. wavelength and delay. In one embodiment, the beams
are overlapped at an angle so that a selected range of delay times
is within the intersection to produce a simultaneous output over
the time delays of interest.
Inventors: |
Kane; Daniel J. (Santa Fe,
NM), Trebino; Rick P. (Livermore, CA) |
Assignee: |
The Regents of the University of
California (Los Alamos, NM)
Sandia National Laboratory (Los Alamos, NM)
|
Family
ID: |
25511693 |
Appl.
No.: |
07/966,644 |
Filed: |
October 26, 1992 |
Current U.S.
Class: |
356/450;
356/520 |
Current CPC
Class: |
G01J
11/00 (20130101) |
Current International
Class: |
G01J
11/00 (20060101); G01B 009/02 () |
Field of
Search: |
;356/354,345,347,351,353 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Malcolm Gower, "Phase Conjugate Mirrors," Tutorial T8 pp. 1-5.
.
Rick Trebino et al., "Chirp and Self Phase Modulation in Induced
Grating Autocorrelation Measurements of Ultrashort Pulses," 15 Opt.
Lett. No. 19, pp. 1079-1081 (October 1990). .
Rick Trebino et al., "Forth Order Partial Coherence Effects in the
Formation of Integrated Intensity Gratings w/Pulsed Light Sources,"
3 J. Opt. Soc. Am. B, pp. 1295-1304 (Oct. 1986). .
Jean Paul Foing et al., "Femtosecond Pulse Phase Measurement by
Spectrally Resolved Up Conversion: Appl. to Continuum Compression,"
28 IEEE J. Quantum Electron., No. 10, pp. 2285-2290. .
A. Brun et al., "Single-shot Characterization of Ultrashort Light
Pulses," 24 J. Phys. D: Appl. Phys., pp. 1225-1233 (1991). .
H. J. Eichler et al., Laser-Induced Dynamic Gratings,
Springer-Verlag, New York (1988), pp. 1-37. .
Juan L. A. Chilla et al., "Direct Determination of the Amplitude
and the Phase of Femtosecond Light Pulses," 16 Opt. Lett., No. 1,
pp. 39-41 (1991) ..
|
Primary Examiner: Turner; Samuel A.
Attorney, Agent or Firm: Wilson; Ray G.
Claims
What is claimed is:
1. A method for measuring the intensity and phase of a light pulse,
comprising the steps of:
inputting said light pulse to form a probe pulse;
providing a gate pulse having a variable time delay;
combining said gate pulse and said probe pulse within an
instantaneously responding nonlinear medium to form a signal pulse
functionally related to a temporal slice of said probe pulse
corresponding to the time delay between said probe pulse and said
gate pulse;
inputting said signal pulse to a wavelength selective device to
output signal pulse field information comprising signal intensity
vs. frequency for a first value of said time delay; and
varying said time delay over a range of values effective to yield
an intensity plot of signal intensity vs. frequency and delay.
2. A method according to claim 1, further including the steps of
extracting the shape of said light pulse as intensity vs. time and
phase vs. time from said pulse field information.
3. A method according to claim 1, wherein said gate pulse is formed
by splitting said light pulse to form said gate pulse and said
probe pulse.
4. A method according to claim 1, further including the step of
relatively polarizing said gate pulse and said probe pulse.
5. A method according to claim 1, wherein said step of combining
said gate pulse and said probe pulse into said nonlinear medium
includes the step of mapping a relative time delay between said
gate pulse and said probe pulse onto spatial coordinates where the
intersection of said gate pulse and said probe pulse in said
nonlinear medium represents a range of delay times between said
gate and probe pulses.
6. A method according to claim 4, further including the steps of
extracting the shape of said light pulse as intensity vs. time and
phase vs. time from said pulse field information.
7. A method according to claim 5, wherein said gate pulse is formed
by splitting said light pulse to form said gate pulse and said
probe pulse.
8. A method according to claim 4, wherein said step of combining
said gate pulse and said probe pulse into said nonlinear medium
includes the step of mapping a relative time delay between said
gate pulse and said probe pulse onto spatial coordinates where the
intersection of said gate pulse and said probe pulse in said
nonlinear medium represents a range of delay times between said
gate and probe pulses.
9. A method according to claim 8, further including the steps of
extracting the shape of said light pulse as intensity vs. time and
phase vs. time from said pulse field information.
10. A method according to claim 8, wherein said gate pulse is
formed by splitting said light pulse to form said gate pulse and
said probe pulse.
11. A method according to claim 2, wherein said steps of extracting
said shape of said light pulse further comprises the steps of:
forming an initial guess E.sup.(0) (t) to represent said light
pulse;
calculating an iteration of E.sup.(0).sub.sig (t,.tau.) from
E.sup.(0) (t);
transforming said iteration of E.sup.(0).sub.sig (t,.tau.) to
E.sup.(0).sub.sig (.omega.,.tau.);
replacing the magnitude of E.sup.(0).sub.sig (.omega.,.tau.) with
the square root of the measured value of I.sub.FROG (.omega.,.tau.)
and performing an inverse Fourier transform to provide a
replacement function E.sup.(1) (t) for said initial guess; and
performing the above steps until said replacement function
E.sup.(1) (t) converges to a final function.
12. A method according to claim 6, wherein said steps of extracting
said shape of said light pulse further comprises the steps of:
forming an initial guess E.sup.(0) (t) to represent said light
pulse;
calculating an iteration of E.sup.(0).sub.sig (t,.tau.) from
E.sup.(0) (t);
transforming said iteration of E.sup.(0).sub.sig (t,.tau.) to
E.sup.(0).sub.sig (.omega.,.tau.);
replacing the magnitude of E.sup.(0).sub.sig (.omega.,.tau.) with
the square root of the measured value of I.sub.FROG (.omega.,.tau.)
and performing an inverse Fourier transform to provide a
replacement function E.sup.(1) (t) for said initial guess; and
performing the above steps until said replacement function
E.sup.(1) (t) converges to a final function.
13. A method according to claim 9, wherein said steps of extracting
said shape of said light pulse further comprises the steps of:
forming an initial guess E.sup.(0) (t) to represent said light
pulse;
calculating an iteration of E.sup.(0).sub.sig (t,.tau.) from
E.sup.(0) (t);
transforming said iteration of E.sup.(0).sub.sig (t,.tau.) to
E.sup.(0).sub.sig (.omega.,.tau.);
replacing the magnitude of E.sup.(0).sub.sig (.omega.,.tau.) with
the square root of the measured value of I.sub.FROG (.omega.,.tau.)
and performing an inverse Fourier transform to provide a
replacement function E.sup.(1) (t) for said initial guess; and
performing the above steps until said replacement function
E.sup.(1) (t) converges to a final function.
14. Apparatus for measuring the intensity and phase of a light
pulse, comprising:
means for inputting said light pulse to form a probe pulse;
means for inputting a gate pulse;
delay means for variably delaying said gate pulse;
combining means for overlapping said gate pulse and said probe
pulse;
an instantaneously responding medium located for receiving said
combined pulses and outputting a signal pulse functionally related
to said combined pulses; and
a wavelength-selective device for receiving said signal pulse and
spectrally resolving said signal pulse into signal intensity vs.
wavelength.
15. Apparatus according to claim 14, further including polarization
means for relatively polarizing said gate pulse and said probe
pulse.
16. Apparatus according to claim 14, further including means for
splitting said light pulse to form said gate pulse and said probe
pulse.
17. Apparatus according to claim 14, wherein said combining means
comprises means for propagating said gate pulse and said probe
pulse at an angle therebetween to map delay times onto separated
spatial coordinates in said medium.
18. Apparatus according to claim 17, further including means for
splitting said light pulse to form said gate pulse and said probe
pulse.
19. Apparatus according to claim 14, wherein said
wavelength-selective device includes imaging means for receiving
said signal pulse and forming an image to display signal intensity
vs. wavelength and delay.
Description
BACKGROUND OF THE INVENTION
This invention relates to the measurement of parameters for
ultrashort pulses and, more particularly, to the measurement of
data that directly yields the pulse shape and phase of ultrashort
light pulses. This invention is the result of a contract with the
Department of Energy (Contract No. W-7405-ENG-36).
The generation of ultrashort laser pulses, i.e., laser pulse widths
shorter than a few picoseconds, has been under development for some
time and it is now possible to obtain ultrashort pulses over a
relatively wide range of wavelengths. Measurement techniques to
characterize these ultrashort pulses has not developed accordingly,
however. The problem is difficult because the durations of
ultrashort pulses are much less than the temporal resolution of
available measuring devices. Early characterization techniques
generated an intensity autocorrelation only, and later developments
have allowed the determination of various phase distortions common
to ultrashort pulses by, for example, such methods as
interferometric autocorrelations or degenerate-four-wave mixing
processes.
In a classic autocorrelator, an incoming laser pulse is split into
two identical pulses. The two pulses arrive at a doubling crystal
at the same time and intersect to output second harmonic light. The
intensity of the second harmonic light is measured as a function of
delay between the two pulses. This yields an intensity
autocorrelation. An interferometric autocorrelation can be produced
when the delay is stepped at a fraction of a wavelength while the
device is stable and the fringes are observed.
Neither intensity autocorrelation nor interferometric
autocorrelation provides either the pulse intensity or the phase of
the pulse, however. Further, stability of interferometric
autocorrelation to less than one wavelength of light is required.
Special materials are required to generate the second harmonic
output and available materials limit the technique to regions above
400 nm in wavelength. Finally, autocorrelation provides only a very
approximate indication of the pulse width and phase information is
not available to extract any additional information from the
autocorrelation. Interferometric autocorrelation does give some
phase information, but cannot, for example, distinguish positive
from negative chirp.
A recent development reported by J. L. A. Chilla et al., "Direct
Determination of the Amplitude and the Phase of Femtosecond Light
Pulses," 16 Opt. Lett., No. 1, pp. 39-41 (1991), provides a method
for directly obtaining the pulse shape and phase in the frequency
domain. The method involves frequency-filtering the pulse and
cross-correlating the filtered pulse with the shorter unfiltered
pulse, yielding the time vs. frequency, which is integrated to
yield the phase vs. frequency. This result, in conjunction with the
spectrum, is the pulse field in the frequency domain. Fourier
transformation then yields the intensity and phase in the time
domain. While the disclosed method does provide structural
information on ultrashort pulses, the method is complex and
time-consuming to perform and requires multiple pulses to develop
the required information.
Yet another technique for characterization of single ultrashort
pulses is reported by A. Brun et al., "Single-shot Characterization
of Ultrashort Light Pulses," 24 J. Phys. D: Appl. Phys., pp.
1225-1233 (August 1991). A beam splitter produces two replicas of
the incident pulse. In one embodiment, one of the beams is focused
in a water cell to output a pulse with a continuum chirp, i.e.,
different frequencies are distributed along the continuum temporal
profile. This continuum pulse is then linearly polarized and
combined with the other beam in a Kerr medium to transform the
temporal modulation of the pulse into a spectral modulation. A
spectrograph converts the wavelength-encoded temporal information
to the spatial domain for readout. While spatial information may be
obtained for a single pulse, multiple pulses are needed to first
characterize the continuum. Further, a portion of the continuum
having a linear chirp must be used. A variety of pump pulse delays
were used to verify that the measured response was only slightly
dependent on delay so long as the chirp was generally linear over
the central wavelength selected for beam crossing. A good
approximation of the ultrashort light pulse temporal shape is
reported, but this method did not produce phase information.
Accordingly, it is an object of the present invention to obtain
intensity and phase information of an ultrashort light pulse using
direct measurement techniques.
It is another object of the present invention to obtain intensity
and phase information of an ultrashort pulse using spectrally
resolved nonlinear optical spectroscopy techniques.
One other object of the present invention is to obtain intensity
and phase information of single ultrashort pulse.
Yet another object of the present invention is to obtain an
intuitive display that embodies phase and intensity characteristics
of ultrashort pulses.
Additional objects, advantages and novel features of the invention
will be set forth in part in the description which follows, and in
part will become apparent to those skilled in the art upon
examination of the following or may be learned by practice of the
invention. The objects and advantages of the invention may be
realized and attained by means of the instrumentalities and
combinations particularly pointed out in the appended claims.
SUMMARY OF THE INVENTION
To achieve the foregoing and other objects, and in accordance with
the purposes of the present invention, as embodied and broadly
described herein, the present invention may comprise a method and
apparatus to directly obtain intensity and phase information of an
ultrashort light pulse. An input light pulse is formed into a probe
pulse. A gate pulse is provided with a variable delay relative to
the probe pulse. The gate pulse and the probe pulse are then
combined in an instantaneously responding nonlinear medium to form
a signal pulse representing the probe pulse characteristics at a
time functionally related to the delay of the gate pulse to provide
a series of temporal slices of the probe pulse. A spectrometer
receives the output pulse to generate an intensity signal as a
function of delay and wavelength.
In one embodiment, the gate pulse is delayed with various values to
provide an intensity plot of signal intensity vs. wavelength and
gate pulse delay. In another embodiment, the gate pulse and probe
pulse are propagated through the nonlinear element at an angle to
output a linear spatial signal having a range of gate pulse delay
times that directly yields the plot of signal intensity vs.
wavelength and gate pulse delay on a single pulse.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and form a
part of the specification, illustrate embodiments of the present
invention and, together with the description, serve to explain the
principles of the invention. In the drawings:
FIG. 1 schematically illustrates an ultrashort pulse characterizing
device according to one embodiment of the present invention.
FIG. 2 graphically depicts the sampled pulse output from the
nonlinear medium.
FIGS. 3A-3F pictorially shows the optical record of the intensity
plot of frequency vs. time delay for various input pulse
characteristics.
FIG. 4. schematically illustrates an ultrashort light pulse
characterizing device according to a second embodiment of the
present invention that can characterize a single pulse.
FIGS. 5A-5D graphically depict theoretical derivations of pulse
shape information using theoretical output according to the present
invention.
FIGS. 6A-6D graphically depict an actual FROG output and derived
pulse shape and phase information using noise as an initial
guess.
DETAILED DESCRIPTION OF THE DRAWINGS
The present invention provides a method, referred to herein as a
frequency-resolved optical grating (FROG), to directly determine
the intensity and phase of an ultrashort light pulse. FROG acts to
provide an output signal or display related to the spectrogram of
the pulse. FROG then uses phase retrieval techniques to obtain the
intensity, I(t), and phase, .phi.(t), of the pulse. Two pulses are
combined in a nonlinear optical medium: one variably delayed pulse
acts as a gate pulse and the pulse to be measured is the probe
pulse which is gated by the gate pulse in the nonlinear optical
medium. The resulting signal-pulse electric field for an optical
Kerr effect embodiment is given by
other nonlinear optical responses.
The output signal spectrum is then a function of the delay between
the two input pulses, i.e., a series of temporal slices of the
probe pulse. The measured signal, I.sub.FROG, is a function of
frequency, .omega., and delay, .tau.:
The full pulse field is essentially uniquely determined by the FROG
output, even for pathological pulse shapes and/or phases, as shown
by rewriting Equation (1) as a two-dimensional phase retrieval
problem:
where E.sub.sig (t,.OMEGA.) is the one-dimensional Fourier
transform of E.sub.sig (t,.tau.) with regard to the delay variable,
.tau.. Thus, unique solutions for E.sub.sig (t,.OMEGA.) exist in
essentially all cases. In addition, it is straightforward to obtain
E(t) from E.sub.sig (t,.tau.):
where .epsilon. is inversely proportional to the pulse energy per
unit area, a constant. Slightly different expressions may result
for E(t) for different nonlinear effects or geometries.
While a variety of ways exist to find E(t) from E.sub.sig
(.OMEGA.,.tau.), a phase-retrieval algorithm is the preferred
method. Such algorithms require a constraint of some nature. Here,
the form of the signal field E.sub.sig (t,.tau.) is a constraint on
the solution. Thus, an estimate for E.sub.sig (t,.tau.) gives an
estimate for E(t), which can then be used to give a new estimate
for E.sub.sig (t,.tau.).
In a preferred form of solution, a simple iterative one dimensional
Fourier-transform algorithm is used and involves Fourier
transforming back and forth between E.sub.sig (t,.tau.) and
E.sub.sig (.omega.,.tau.). In the .omega.-domain, the magnitude of
Equation (2) is replaced with the square root of I.sub.FROG
(.omega.,.tau.). The above constraint on the form of the signal
field is used in the t-domain, generating the (k+1)st iteration for
E.sub.sig (t,.tau.) by first setting:
Using E.sub.sig
(t,.tau.).alpha.E(t).vertline.E(t-.tau.).vertline..sup.2, the
(k+1)st iteration for E.sub.sig (t,.tau.) is constructed:
The application of the iterative algorithm shown in Equations (4)
and (5) requires an initial "guess" for E(t). The preferred initial
guess E(.sup.0) (t) for all cases has been found to be noise. The
initial guess is input to Equation (5) to derive an
E(.sup.0).sub.sig (t,.tau.). A one dimensional Fourier transform is
then performed to provide E.sup.(0).sub.sig (.omega.,.tau.). The
magnitude of E.sup.(0).sub.sig (.omega.,.tau.) is then replaced
with the square root of the detected signal I.sub.FROG
(.omega.,.tau.) and the resulting E'.sup.(0).sub.sig
(.omega.,.tau.) is inverse transformed to provide
E'.sup.(0).sub.sig (t,.tau.) for input to Equation (4) to form
E(.sup.1) (t). The iterations continue until the results
converge.
An alternative initial guess can be produced in the following
manner. The approximate pulse time vs. frequency, t(.omega.), is
given by:
Integration of t(.omega.) yields the approximate pulse phase vs.
frequency, .psi.(.tau.). The pulse spectrum, I(.omega.), is also
naturally obtained by FROG, either precisely by a separate and
simultaneous measurement or approximately by integrating I.sub.FROG
(.omega.,.tau.) with respect to .tau. and deconvolving out the
intensity autocorrelation. These results yield the approximate full
amplitude and phase of the pulse field in the frequency domain,
E(.omega.). Fourier transformation then yields an approximate
result for E(t). Generally, however, noise provides an initial
guess that rapidly converges to a pulse shape using Equation (5)
and a more precise guess is not necessary.
One embodiment of FROG apparatus 10 is shown in FIG. 1. An
ultrashort light pulse 12 is input to beam splitter 14 to form
probe pulse 13 and gate pulse 15. Probe pulse 13 is directed by
optical alignment system 16 through lens 22 into instantaneously
responding nonlinear medium 24. Gate pulse 15 is provided with a
variable delay .tau. by delay 18. The probe pulse and the gate
pulse are focused into nonlinear medium 24 through lens 22. Thus,
beams having electric fields E(t) and E(t-.tau.) intersect in
nonlinear medium 24.
The interaction of two laser beams in a nonlinear medium is well
known, e.g., H. J. Eichler et al., Laser-Induced Dynamic Gratings,
Springer-Verlag, N.Y. (1988). The interaction of the beams produces
an induced grating in the medium so that an incident probe beam,
E(t), can be diffracted by a gating beam, E(t-.tau.), during the
period of beam coincidence. Thus, only a temporal slice of the
probe beam may be selected by the gating beam as graphically shown
in FIG. 2. For not-too-pathological pulse shapes, the gate will be
centered at and have maximum strength at about the time (.tau./2),
i.e., the midpoint between pulse peaks. The probe pulse will
typically have an intensity gradient at this time, however, so the
component of the probe pulse contributing the most intensity to the
diffracted pulse will be at .apprxeq..tau./3 (an exact result for
Gaussian-intensity pulses). The instantaneous frequency of the
probe pulse is selected at that time, as a result.
Referring again to FIG. 1, in accordance with the present invention
the diffracted pulse is directed by output optics 28 to a
wavelength-selective device 32, e.g., a spectrometer, to resolve
the frequency components in the selected temporal slice of probe
pulse 13. Camera 34 records the spectrum as a function of time
delay of probe pulse 13 to produce an intensity plot vs. frequency
and delay. FIGS. 3A-3F graphically illustrate the output results
for various characteristics of femtosecond pulse 12. FIG. 3A
depicts a negatively chirped pulse, i.e., a pulse with decreasing
frequency with time; FIG. 3C depicts an unchirped pulse, i.e., a
constant frequency pulse; and FIG. 3E depicts a positively chirped
pulse, i.e., a pulse with increasing frequency with time. FIGS. 3B,
3D, and 3F are the corresponding camera 34 records of intensity as
a function of frequency and delay and illustrate that the present
technique uniquely and directly determines the phase
characteristics of the femtosecond pulse. As hereinafter shown,
these plots further contain all of the information necessary to
reconstruct the intensity and phase characteristics of the incident
pulse.
By way of example, a system according to FIG. 1 was constructed to
measure a Rhodamine-6G colliding-pulse mode-locked laser producing
<100-fsec pulses at a repetition rate of about 100 MHz amplified
to an energy of about 200 .mu.J. A beam splitter 14 and neutral
density filters (not shown) yielded two pulses of about 6 .mu.J
each. A high quality variable delay 18, with a resolution of 1
.mu.m, produced the variable delay for one pulse train. A lens 24
with a focal length of 1-m focused and crossed the two beams at an
angle of about 0.5.degree.. The electronic Kerr effect in a 3-mm
thick BK-7 window placed at the focus of these two beams provided
self-diffraction with about 10.sup.-4 efficiency. The peak
intensity at the BK-7 window was approximately 100 GW/cm.sup.2. The
diffracted beam 26 was attenuated (ND 1.0), reflected by mirrors
28, and focused onto the 50-.mu.m slits of a 1/4-m Jarrel Ash
spectrometer 32. A Photometrics CCD camera collected the dispersed
diffracted light, averaged over 20 shots. The diffracted intensity
vs. wavelength was then output to a computer for analysis.
The above system was used to obtain diffracted-pulse spectra at
eleven different delays at 67-fsec intervals using the
unrecompressed, positively chirped pulses of about 300-fsec width.
The spectra clearly revealed a large wavelength chirp over the
range of delays. From the measured diffracted-pulse wavelength vs.
delay the approximate pulse wavelength vs. time was derived.
Inverting this latter result yielded the pulse time and phase vs.
wavelength, which, after inverse-Fourier transformation, yielded
pulse intensity vs. time. This computed pulse intensity vs. time
was in good agreement with an experimentally determined
autocorrelation using conventional second-harmonic generation. The
system has also been used with fully compressed, transform-limited
pulses and pulses with negative chirp, with expected results in all
cases.
Another embodiment of an optical grating device useful for single
pulse analysis is shown in FIG. 4 as FROG apparatus 36. Incoming
pulses are provided as probe light pulse 38 and gate light pulse 42
as shown in FIG. 1, where probe light pulse 38 is an ultrashort
light pulse whose pulse characteristics are to be determined. Gate
pulse 42 may be formed from the same light pulse as pulse 38 or may
originate from an independent source. Gate pulse 42 is polarized to
45.degree. by polarizer 45 and probe pulse 38 is vertically
polarized by polarizer 44. If gate pulse 42 is nominally polarized
(more than about 90%), the polarization may be rotated 45.degree.
by changing the direction of the pulse by 90.degree. after an
initial change of direction, up or down, by 45.degree..
Polarized gate pulse 42 and probe pulse 38, which are propagating
at an angle to one another, are overlapped into nonlinear optical
medium 48. The effect of overlapping the pulses at an angle is to
map a range of time delays between the two beams onto spatial
coordinates within medium 46 to provide spatial resolution over the
range of time delays. In other words, as shown in FIG. 4, the
intersection of probe pulse 38 and gate pulse 42 in nonlinear
medium 48 provides a portion where gate pulse 42 leads probe pulse
38 (the upper region as shown) and a portion where probe pulse 38
leads gate pulse 42 (the lower region as shown). In one embodiment,
a cylindrical lens of focal length 10 cm focused the two beams to
increase the intensity of the pulses at nonlinear medium 48 and
increase the resulting signal 60 intensity. The two beams crossed
at an angle of about 20.degree., yielding a range of delays of
about 1.2 psec.
Signal light output from nonlinear medium 48 is input to polarizer
52, which rejects any component 54 of the vertically polarized
probe pulse 38 and passes the signal pulse 60, which has horizontal
polarization. Signal pulse 60 is then focused through imaging lens
58 into the input slit of imaging spectrometer 62. Spectrometer 62
forms an output intensity distribution vs. wavelength and time
delay for recordation by CCD camera 64. It will be appreciated that
crossing the beams at a large angle enables the characteristics of
a single pulse to be determined since a range of delay times is
inherent in the intersection of the beams. A cylindrical lens may
be used to increase signal intensity if needed.
FIGS. 5A through 5D graphically illustrate the capability of the
apparatus 36 shown in FIG. 4 and the algorithm of equations (1)
through (6) to determine the characteristics of an ultrashort light
pulse. FIGS. 5A-5D show theoretical results using the algorithm for
two commonly encountered ultrashort pulses, (1) a nearly square
pulse intensity with linear chirp (FIGS. 5A and 5B) and (2) a
Gaussian intensity with positive linear chirp (FIGS. 5C and 5D).
FIG. 5A illustrates an initial guess for a pulse shape involving
the correct phase but a Gaussian intensity and the iterative
evolution to a pulse shape that is very nearly the correct pulse
shape. FIG. 5B illustrates the relatively rapid convergence of the
algorithm. FIG. 5C illustrates an initial guess involving the
correct intensity, but with a very bad estimate of the phase, i.e.,
the correct magnitude but opposite sign. Again, as shown in FIG.
5D, the algorithm converged to the correct phase in relatively few
iterations.
A FROG output for an actual single positively chirped pulse about
100-fsec in duration is shown in FIG. 6A. The positive chirp is
clearly seen. FIGS. 6B and 6C illustrate the pulse characteristics
I(t) and .phi.(t). Use of the algorithm on FIG. 6A data points
extracts the pulse shape I(t) shown in FIG. 6B with a pulse width
of about 110-fsec (FWHM). Noise was used as the initial guess for
the pulse and convergence occurred in 50 iterations. The derived
phase evolution .phi.(t) is shown in FIG. 6C. The inverted
parabolic shape indicates positive chirp, that is, linearly
increasing frequency vs. time, as also indicated by FIG. 6A. As a
check of the FROG output, the pulse third-order intensity
autocorrelation was computed and compared with the simultaneously
obtained experimental third-order intensity autocorrelation
obtained by integrating the FROG output over frequency for a given
value of the delay. A good agreement between the computed and
measured values is apparent from FIG. 6D.
Thus, a method and apparatus for determining the intensity and
phase of femtosecond pulses using a frequency resolved optical
gating has been described herein. The FROG technique is relatively
simple to implement, has zero or negligible phase-mismatch, and is
very broadband. Also, the technique is well-suited to the UV
spectral range of femtosecond pulses since diffraction efficiencies
are relatively high in that wavelength range.
The technique according to the present invention is particularly
adapted to single shot measurements rather than the "average"
measurements required in the prior art. It will be understood,
however, that multishot pulse trains can be analyzed according to
the method and apparatus described herein. In the case of a
multishot pulse train, the derived intensity and phase information
is the average intensity and phase of the pulse train and not the
intensity and phase of any single pulse.
As used herein, the term "ultrashort" refers to pulse durations
shorter than a few tens of picoseconds. These are the pulses of
interest to measure and are well within the regime of pulses that
can be analyzed from the FROG data. Long pulses can also be
analyzed according to the present invention, but such pulses can be
easily analyzed using existing technology. It should be noted that
there is no fundamental limit to the wavelength of the pulse to be
measured. Limiting factors are the detectors and spectrometers and
not the FROG technique. Thus, the above technique may be used, for
example, in the vacuum UV and x-ray regions of the spectrum when
suitable detectors and nonlinear materials become available.
As noted, the preferred form of light pulse is a laser light pulse
since laser light is generally coherent. In principle, any
ultrashort light pulse can be measured using FROG. Practically
speaking, however, any ultrashort light pulse with enough intensity
to be measured via FROG will be produced in some way by a laser.
Further, any lack of spatial coherence may degrade the quality of
the measurement. The temporal response of the nonlinear optical
medium is loosely referred to as an instantaneous response. The
desired material should have a response that is faster than the
duration of the pulse, although a response on the order of the
pulse duration can be accommodated.
A preferred nonlinearity is associated with x.sup.(3) since it
provides relatively higher signal levels. Any odd x will provide
the same information, but with weaker signals. Even x's will not
provide information on even phase distortions, but information on
odd phase distortions may have use in some applications.
The preferred embodiments described herein use a single light pulse
to form both a probe pulse and a gate pulse. It will be understood
that the probe pulse and the gate pulse may originate from
independent ultrashort light pulses. Then, the pulse shape, i.e.,
intensity vs. time of an independent gate pulse must be known.
The foregoing description of preferred embodiments of the invention
have been presented for purposes of illustration and description.
It is not intended to be exhaustive or to limit the invention to
the precise form disclosed, and obviously many modifications and
variations are possible in light of the above teaching. The
embodiments were chosen and described in order to best explain the
principles of the invention and its practical application to
thereby enable others skilled in the art to best utilize the
invention in various embodiments and with various modifications as
are suited to the particular use contemplated. It is intended that
the scope of the invention be defined by the claims appended
hereto.
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